Abstract

The optical properties of three-dimensional woodpile photonic crystals (PhCs) composed of circular cylinder rods with a planar defect structure at the central layer are theoretically investigated using the parallel finite-difference time-domain method and plane-wave expansion method. Three types of planar defects are introduced into the PhC by alternating respectively the dielectric constant, cylinder diameter, and misalignment of the rods at the defect layer. The transmission spectrum and band diagram of each planar defect structure are systematically studied. The resonance and transmission properties of the defect structures can be characterized by two distinct resonant modes, the defect mode and the band-edge resonant mode, which have been identified by detailed spectrum analysis, calculated mode profiles and field patterns. It is shown that, by modifying the rod diameter or the dielectric constant of materials at the defect layer, the resonant modes can be varied and controlled. Also, by applying dislocation to a layer of dielectric rods, the photonic band edges can be shifted.

Transmission spectrum of the (C)4(D)1(C)4 sandwich PhCs with εd≤ε. The plane wave source incident along the z axis is with (a) Ex polarization (perpendicular to the defect rods) and (b) Ey polarization (parallel to the defect rods). The electric field pattern (c) is with εd=0.25ε and Ey polarization with frequency fm=0.5093(c/a), according to the transmitted peak shown in Fig. 5a.

Transmission spectrum of the (C)4(D)1(C)4 sandwich PhCs with εd≥ε. The incident plane wave source is vertical with (a) Ex polarization and (b) Ey polarization. Electric field patterns of the εd=2.0ε and the incident plane wave source with fm frequency is vertical with (c) Ex polarization, fm=0.6170(c/a), (d) Ey polarization, fm=0.6134(c/a), and (e) Ey polarization, fm=0.6611(c/a). The frequencies of the plane wave source are selected according to the transmitted peaks shown in Fig. 5b.

Transmission spectrum of (C)4(D)1(C)4 sandwich PhCs with rd≤r. The incident plane wave source is vertical with (a) Ex polarization and (b) Ey polarization. (c) Electric field pattern with rd=0.50r and Ey polarization with frequency fm=0.5133(c/a), which is according to the transmitted peaks shown in Fig. 8a.

Transmission spectrum of (C)4(D)1(C)4 sandwich PhCs with rd≥r. The incident plane wave source is vertical with (a) Ex polarization and (b) Ey polarization. Electric field patterns of the rd=2.0r and the incident plane wave source is vertical with (c)–(e) Ex polarization and (f), (g) Ey polarization. The frequencies are selected as (c) fm=0.5001(c/a), (d) fm=0.5302(c/a), (e) fm=0.6111(c/a), (f) fm=0.4769(c/a), and (g) fm=0.6411(c/a), which are according to the transmitted peak shown in Fig. 8b.